Quasinormal modes in Schwarschild black holes due to arbitrary spin fields

The Newman-Penrose formalism is used to deal with the massless scalar, neutrino, electromagnetic, gravitino and gravitational quasinormal modes (QNMs) in Schwarzschild black holes in a united form. The quasinormal mode frequencies evaluated by using the 3rd-order WKB potential approximation show that the boson perturbations and the fermion perturbations behave in a contrary way for the variation of the oscillation frequencies with spin, while this is no longer true for the damping's, which variate with $s$ in a same way both for boson and fermion perturbations.Comment: 11 pages, 3 figure

Doctor of Philosophy

dissertationThe purpose of this dissertation was to examine the effects of Sports, Play and Active Recreation for Kids (SPARK), a health-related physical fitness school program, on middle school students' in-class physical activity levels, cardiovascular fitness levels, motivation, and academic learning time compared to the traditional physical education program. Two quantitative studies were conducted to address this purpose. In study 1, in-class physical activity levels (step counts measured by pedometer), cardiovascular fitness levels (measured by PACER of FITNESSGRAM), and motivation (perceived competence and enjoyment) were assessed among 174 middle school children from SPARK and traditional physical education groups over a period of 11 weeks. Change scores for each outcome variable were used for data analysis. Results from a MANOVA yielded that the SPARK program was more effective in increasing students' in-class physical activity and cardiovascular fitness levels compared to the traditional physical education program, achieving a statistically significant greater increased change score on in-class physical activity levels (Mean Δ = 9.33) compared to the traditional physical education group (Mean Δ = 1.30) (p < .05). Study 2 examined the impact of SPARK and traditional physical education on students' percentage of time spent in academic learning in physical education over the course of 9 weeks. The results suggested that the SPARK program was more effective in augmenting students' percentage of time spent in subject matter motor, especially in skill practice and fitness, compared to the traditional physical education program. This finding is consistent with previous research regarding the in-class physical activity levels in study 1. In conclusion, these studies support that SPARK is an effective pedagogical strategy to increase middle school children's physical activity levels, cardiovascular fitness, and academic learning time in school physical education settings. Physical educators may consider SPARK as an alternative instructional program in order to sustain elevated levels of physical activity, cardiovascular fitness and academic learning time in their classes. By employing SPARK children will have a greater probability of achieving recommended physical activity and cardiovascular fitness levels suggested by various health agencies